Conjunto de alcanzabilidad de un sistema mecánico controlable y condiciones de estabilidad robusta
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https://doi.org/10.4995/riai.2020.11938Palabras clave:
Ecuaciones diferenciales, sistemas de control no lineal, perturbaciones, estabilidadResumen
En este trabajo se determina de forma numérica la frontera del conjunto de alcanzabilidad de una ecuación diferencial de segundo orden con una perturbación externa, empleando la solución del problema de la variación máxima de las amplitudes de oscilación de sus soluciones. El método consiste en determinar en un conjunto de funciones dado, la perturbación externa que provoque amplitudes de oscilación máxima en las soluciones de la ecuación diferencial que describe, como caso particular, la dinámica de un sistema mecánico controlable con impactos. Con ayuda de esta perturbación, se determina la existencia de una trayectoria cerrada que describe la frontera del conjunto de alcanzabilidad, lo cual permite establecer condiciones suficientes sobre la estabilidad robusta de las soluciones de la ecuación diferencial. Los resultados se ilustran de forma numérica en casos particulares.
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